My (potentially unpopular) feeling about GEB is that it's a book that explores some very interesting areas but that doesn't say all that much of interest itself. Reading it I felt like different sections could be put into two categories: (good and somewhat romantic) exposition about something interesting, and observations that seem profound until you think about them and realize that they're stupid (e.g. Hofstadter spends some time discussing how a Bach piece that ends up one semitone higher than it starts [and can therefore be repeated to form an infinite ascension] embodies self-referentiality and that this is the critical component of self-awareness, and that therefore the two are connected; of course, this is all just more-or-less meaningless fluff).

So I'd say skip it.